The Order of Time

by Carlo Rovelli

Time that is determined in this way by a macroscopic state is called “thermal time.” In what sense may it be said to be a time? From a microscopic point of view, there is nothing special about it—it is a variable like any other. But from a macroscopic one, it has a crucial characteristic: among so many variables all at the same level, thermal time is the one with behavior that most closely resembles the variable we usually call “time,” because its relations with the macroscopic states are exactly those that we know from thermodynamics.

Toothpaste leaving a tube - macroscopic state changes that are easy to define at a specific level in isolation

But it is not a universal time. It is determined by a macroscopic state, that is, by a blurring, by the incompleteness of a description. In the next chapter, I will discuss the origin of this blurring, but before I do, let’s take another step by bringing quantum mechanics into consideration.

Thermal time treats regions which adhere to a conservation rule as finite state spaces such that time exists as the frequency of transitions between defined states within the region. A region is of course 'blurred' by its own lack of defining composition and its interaction with other regions. If this system could be isolated, it's entropy would be tied to the rate of transitions between defined states - with the caveat that describable 'states' could only be locally defined (as a consequence of relativity discussed earlier).

This is called the “noncommutativity” of the quantum variables, because position and speed “do not commute,” that is to say, they cannot exchange order with impunity. This noncommutativity is one of the characteristic phenomena of quantum mechanics. Noncommutativity determines an order and, consequently, a germ of temporality in the determination of two physical variables. To determine a physical variable is not an isolated act; it involves interaction. The effect of such interactions depends on their order, and this order is a primitive form of the temporal order.

It does seem like the direction of time must originate in path dependent and non-commutative phenomenon. Causality is asymmetric as a reflection of thermal time - causes and effects are not interchangeable. The asymmetries of thermal and temporal system are the exception to symmetries in other fundamental phenomenon. Not only is time a local phenomenon but it is also directional.

Between ourselves and the rest of the world there are physical interactions. Obviously, not all the variables of the world interact with us, or with the segment of the world to which we belong. Only a very minute fraction of these variables does so; most of them do not react with us at all. They do not register us, and we do not register them. This is why distinct configurations of the world seem equivalent to us. The physical interaction between myself and a glass of water—two pieces of the world—is independent of the motion of the single molecules of water. In the same way, the physical interaction between myself and a distant galaxy—two pieces of the world—ignores what happens in detail out there. Therefore, our vision of the world is blurred because the physical interactions between the part of the world to which we belong and the rest are blind to many variables. This blurring is at the heart of Boltzmann’s theory.93 From this blurring, the concepts of heat and entropy are born—and these are linked to the phenomena that characterize the flow of time. The entropy of a system depends explicitly on blurring. It depends on what I do not register, because it depends on the number of indistinguishable configurations. The same microscopic configuration may be of high entropy with regard to one blurring and of low in relation to another. This does not mean that blurring is a mental construct; it depends on actual, existing physical interactions.94 Entropy is not an arbitrary ...

Let me summarize the hard ground covered in the last two chapters, in the hope that I have not already lost all my readers. At the fundamental level, the world is a collection of events not ordered in time. These events manifest relations between physical variables that are, a priori, on the same level. Each part of the world interacts with a small part of all the variables, the value of which determines “the state of the world with regard to that particular subsystem.”

Energy (be it mechanical, chemical, electrical, or potential) transforms itself into thermal energy, that is to say, into heat: it goes into cold things, and there is no free way of getting it back from there to reuse it to make a plant grow, or to power a motor. In this process, the energy remains the same but the entropy increases, and it is this which cannot be turned back. The second law of thermodynamics demands it. What makes the world go round are not sources of energy but sources of low entropy. Without low entropy, energy would dilute into uniform heat and the world would go to sleep in a state of thermal equilibrium—there would no longer be any distinction between past and future, and nothing would happen.

Time => Change => interactions => entropy

There are situations that impede and hence slow down the increase of entropy throughout the universe. In the past, for instance, the universe was basically an immense expanse of hydrogen. Hydrogen can fuse into helium, and helium has a higher entropy than hydrogen. But for this to happen, it is necessary for a channel to be opened: a star must ignite for hydrogen to begin to burn there into helium. What causes stars to ignite? Another process that increases entropy: the contraction due to gravity of one of the large clouds of hydrogen that sail throughout the galaxy. A contracted cloud of hydrogen has higher entropy than a dispersed one.97 But the clouds of hydrogen are so vast that they take millions of years to contract. Only after they have become concentrated do they manage to heat up to the point that triggers the process of nuclear fusion. The ignition of nuclear fusion opens the door that allows the further increase in entropy: hydrogen burning into helium.

Gravity as a strictly attractive 'force' (or a consequence of the mass carried by the higgs boson) is the initial and primary driver of entropy in the Universe. It forces things together, and in turn causes their interaction and the transition of the local system into a higher entropy state.

It is entropy, not energy, that keeps stones on the ground and the world turning.

Zero Kelvin - the minimum or maximum entropy state

Since they elaborate possible alternative futures that would follow if the present were exactly as it is except for some detail, we are naturally inclined to think in terms of “causes” that precede “effects”: the cause of a future event is a past event such that the future event would not follow in a world that was exactly the same except for this cause.101 In our experience, the notion of cause is thus asymmetrical in time: cause precedes effect. When we recognize in particular that two events “have the same cause,” we find this common cause102 in the past, not in the future. If two waves of a tsunami arrive together at two neighboring islands, we think that there has been an event in the past that has caused both. We do not look for it in the future. But this does not happen because there is a magical force of “causality” going from the past to the future. It happens because the improbability of a correlation between two events requires something improbable, and it is only the low entropy of the past that provides such improbability. What else could? In other words, the existence of common causes in the past is nothing but a manifestation of low entropy in the past. In a state of thermal equilibrium, or in a purely mechanical system, there isn’t a direction to time identified by causality.

This space—memory—combined with our continuous process of anticipation, is the source of our sensing time as time, and ourselves as ourselves.119 Think about it: our introspection is easily capable of imagining itself without there being space or matter, but can it imagine itself not existing in time?120 It is with respect to that physical system to which we belong—due to the peculiar way in which it interacts with the rest of the world, thanks to the fact that it allows traces and because we, as physical entities, consist of memory and anticipation—that the perspective of time opens up for us, like our small, lit clearing.121 Time opens up our limited access to the world.122 Time, then, is the form in which we beings, whose brains are made up essentially of memory and foresight, interact with the world: it is the source of our identity.123

Our fear of death seems to me to be an error of evolution. Many animals react instinctively with terror and flight at the approach of a predator. It is a healthy reaction, one that allows them to escape from danger. But it’s a terror that lasts an instant, not something that remains with them constantly. Natural selection has produced these big apes with hypertrophic frontal lobes, with an exaggerated ability to predict the future. It’s a prerogative that’s certainly useful but one that has placed before us a vision of our inevitable death, and this triggers the instinct of terror and flight. Basically, I believe that the fear of death is the result of an accidental and clumsy interference between two distinct evolutionary pressures—the product of bad automatic connections in our brain rather than something that has any use or meaning. Everything has a limited duration, even the human race itself.

Be fruitful and multiply, then get out of the way - that is how life thrives